The classification of constant weighted curvature curves in the plane with a log-linear density

Doan The Hieu; Tran Le Nam

doi:10.3934/cpaa.2014.13.1641

Article Contents

2014, Volume 13, Issue 4: 1641-1652. Doi: 10.3934/cpaa.2014.13.1641

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The classification of constant weighted curvature curves in the plane with a log-linear density

Doan The Hieu^1, and
Tran Le Nam^2,

1.
Departement of Mathematics, College of Education, Hue University, Hue
2.
Departement of Mathematics,Dong Thap University, Dong Thap

Received: May 2013

Revised: January 2014

Published: July 2015

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Abstract

In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $R^2.$ The classification gives some interesting phenomena and consequences including: the family of curves converge to a round point when the weighted curvature of curves (or equivalently the forcing term of traveling curved fronts) goes to infinity, a simple proof for a main result in [13] as well as some well-known facts concerning to the isoperimetric problem in the plane with density $e^y.$

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Mathematics Subject Classification: Primary 53C44, 53A04; Secondary 53C21, 35J60.

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References

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